• In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the...
    75 KB (9,506 words) - 17:24, 21 June 2024
  • Thumbnail for Boolean algebra (structure)
    In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...
    49 KB (3,356 words) - 14:42, 23 February 2024
  • a list of topics around Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective...
    6 KB (271 words) - 12:02, 30 October 2023
  • Look up Boolean algebra in Wiktionary, the free dictionary. Boolean algebra is the algebra of truth values and operations on them. Boolean algebra may also...
    547 bytes (104 words) - 12:58, 29 May 2021
  • In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with...
    44 KB (6,241 words) - 10:44, 12 February 2024
  • values (usually "true" and "false") Boolean algebra, a logical calculus of truth values or set membership Boolean algebra (structure), a set with operations...
    2 KB (252 words) - 21:44, 15 January 2024
  • mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct...
    10 KB (1,347 words) - 08:53, 1 December 2023
  • Topological Boolean algebra may refer to: In abstract algebra and mathematical logic, topological Boolean algebra is one of the many names that have been...
    945 bytes (148 words) - 22:45, 2 December 2018
  • logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type...
    27 KB (2,991 words) - 19:39, 17 May 2024
  • An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction...
    12 KB (1,419 words) - 02:48, 30 June 2024
  • In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem...
    5 KB (715 words) - 14:47, 16 January 2024
  • what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras. An interior algebra is an...
    30 KB (3,849 words) - 16:32, 8 April 2024
  • Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued...
    65 KB (8,235 words) - 09:01, 4 February 2024
  • Thumbnail for Boolean function
    logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f : { 0 ...
    23 KB (2,887 words) - 18:33, 15 April 2024
  • In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement...
    15 KB (2,257 words) - 03:04, 29 November 2023
  • Thumbnail for Power set
    the Boolean algebra of the power set of a finite set. For infinite Boolean algebras, this is no longer true, but every infinite Boolean algebra can be...
    20 KB (2,425 words) - 23:34, 3 April 2024
  • Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection...
    15 KB (1,865 words) - 16:28, 28 May 2024
  • In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature ⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨A, ·, +, ',...
    4 KB (435 words) - 03:34, 25 July 2023
  • Boolean algebra Free Boolean algebra Monadic Boolean algebra Residuated Boolean algebra Two-element Boolean algebra Modal algebra Derivative algebra (abstract...
    24 KB (2,084 words) - 23:23, 8 July 2024
  • from a two-element set Boolean operation (Boolean algebra), a logical operation in Boolean algebra (AND, OR and NOT) Boolean operator (computer programming)...
    764 bytes (136 words) - 15:51, 4 October 2021
  • and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The...
    9 KB (1,311 words) - 14:53, 13 July 2023
  • Thumbnail for Ultrafilter
    {\displaystyle {\mathcal {P}}(X),} ordered by set inclusion, is always a Boolean algebra and hence a poset, and ultrafilters on P ( X ) {\displaystyle {\mathcal...
    20 KB (2,957 words) - 22:47, 10 May 2024
  • Thumbnail for George Boole
    George Boole (category Boolean algebra)
    differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854) which contains Boolean algebra. Boolean logic is credited...
    65 KB (7,485 words) - 00:41, 13 July 2024
  • mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen...
    7 KB (795 words) - 00:02, 18 October 2023
  • exactly one of the elements {a, ¬a}, for each element a of the Boolean algebra. In Boolean algebras, the terms prime ideal and maximal ideal coincide, as do...
    13 KB (1,766 words) - 09:56, 30 January 2024
  • Field of sets (redirect from Set algebra)
    play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets. A field of sets...
    23 KB (3,676 words) - 13:27, 30 October 2023
  • In Boolean algebra, the inclusion relation a ≤ b {\displaystyle a\leq b} is defined as a b ′ = 0 {\displaystyle ab'=0} and is the Boolean analogue to the...
    1 KB (210 words) - 20:42, 5 July 2022
  • forms a Boolean algebra, which means that it is closed under the operations of union, intersection, and complementation. This Boolean algebra is the finite–cofinite...
    6 KB (884 words) - 17:19, 18 February 2024
  • Thumbnail for De Morgan's laws
    De Morgan's laws (category Boolean algebra)
    In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid...
    23 KB (3,636 words) - 21:23, 11 July 2024
  • TRUE just when exactly one of its arguments is. Using the laws of Boolean algebra, every propositional logic formula can be transformed into an equivalent...
    52 KB (5,326 words) - 07:49, 3 July 2024